H∞ optimization with time domain constraints over a finite horizon

An algorithm for computing the solution to H_∞ problems with time domain constraints over a finite horizon is presented. This problem is transformed into a convex finite-dimensional optimization problem. Some of the characteristics of the optimal solution are established, namely, the degree of the optimal solution and its behavior in the special case in which the constraints are not binding, in order to gain further insight into the nature of the optimization problem, including the fact that it is in general nondifferentiable. An example is presented in which the technique provides better time responses with only slight deterioration of the robustness properties as compared with the unconstrained H_∞-optimal solution. Although all the results were obtained for single input-single output systems, they extend naturally to multivariable systems